A Derandomized Switching Lemma and an Improved Derandomization of AC0

@article{Trevisan2012ADS,
  title={A Derandomized Switching Lemma and an Improved Derandomization of AC0},
  author={Luca Trevisan and Tongke Xue},
  journal={2013 IEEE Conference on Computational Complexity},
  year={2012},
  pages={242-247}
}
We describe a new pseudorandom generator for AC0. Our generator ε-fools circuits of depth d and size M and uses a seed of length Ŏ(log<sup>d+4</sup> M/ε). The previous best construction for $d \geq 3$ was due to Nisan, and had seed length Ŏ(log<sup>2d+6</sup> M/ε). A seed length of O(log<sup>2d+Ω(1)</sup> M) is best possible given Nisan-type generators and the current state of circuit lower bounds. Seed length Ω(log<sup>d</sup> M/ε) is a barrier for any pseudorandom generator construction… CONTINUE READING
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